论文标题
在与Laplacian和Sturm-Liouville问题I的非本地积分操作员上通勤I：操作员的低级扰动
On a Nonlocal Integral Operator Commuting with the Laplacian and the Sturm-Liouville Problem I: Low Rank Perturbations of the Operator
论文作者
论文摘要
我们将所有一般实际耦合的自我接触边界价值问题重新出发，作为整体运营商，并表明它们都是自由空间绿色功能在实际线路上的有限等级扰动。这个自由空间绿色的函数对应于Saito [N.之前提出的非本地边界值问题。 Saito，应用。计算。 Harmonic Anal。，25，68--97（2008）]。我们证明这些扰动是排名高达4的多项式。它们以相应的边界条件的基本方式封装。
We reformulate all general real coupled self-adjoint boundary value problems as integral operators and show that they are all finite rank perturbations of the free space Green's function on the real line. This free space Green's function corresponds to the nonlocal boundary value problem proposed earlier by Saito [N. Saito, Appl. Comput. Harmonic Anal., 25, 68--97 (2008)]. We prove these perturbations to be polynomials of rank up to 4. They encapsulate in a fundamental way the corresponding boundary conditions.
